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Eprints ID: 3859
To link to this article:
DOI:10.1149/1.3207705
URL:
http://dx.doi.org/10.1149/1.3207705
To cite this version: Xenidou, T. C. and Prud’homme, N. and Aloui, Lyacine and
Vahlas, Constantin and Markatos, N. C. and Boudouvis, A. G. ( 2009) Shape
optimization of a showerhead system for the control of growth uniformity in a MOCVD
reactor using CFD-based evolutionary algorithms. ECS Transactions, vol. 25 (n° 8). pp.
SHAPE OPTIMIZATION OF A SHOWERHEAD SYSTEM FOR THE CONTROL OF GROWTH UNIFORMITY IN A MOCVD REACTOR USING CFD-BASED EVOLUTIONARY ALGORITHMS
T.C. Xenidou1, N. Prud’homme2, L. Aloui2 C. Vahlas2, N.C. Markatos1, A.G. Boudouvis1 1 School of Chemical Engineering, National Technical
University of Athens, 15780 Athens, Greece 2 CIRIMAT-CNRS, ENSIACET, 118 Route de Narbonne,
31077 Toulouse cedex 4, France
Aiming at a high degree of spatial uniformity of the growth rate across the substrate, MOCVD reactors are commonly equipped with showerhead systems above the heated substrates. In these cases, the interplay of chemical reactions and transport phenomena can be controlled through the degree of precursor mixing, as determined by the design of the gas delivery system [1]. Consequently, a shape-optimization problem arises, with regard to the uniformity of the film grown over the substrate.
Most conventional MOCVD systems are designed for a narrow range of operating conditions and, therefore, have limited flexibility for improving the process, particularly regarding the quality of the films. Moreover, the evaluation of the effects of different designs on the process outcome is a task difficult to be addressed by experimental effort. Numerical methods have shown many advantages over trial-and-error experimental methods, as the reactor geometry is easier to be modified and evaluated. To improve the efficiency of computational fluid dynamics (CFD) modeling in the shape design of novel MOCVD systems, an evolutionary algorithm (EA) is incorporated in a CFD software.
The particular MOCVD system under study is described in detail in [2]. The vertical reactor is equipped with a showerhead system above the silicon substrate. The diameters of the susceptor and the shower plate are 58mm and 60mm, respectively. The plate consists of 1450 holes of diameter of 0.76mm. Its thickness is 1mm.
Numerical modeling was used based on the CFD model reported previously [3]. The set of the coupled partial differential equations, along with the boundary conditions, are implemented in PHOENICS software [4]. The optimization analysis was carried out using the optimization platform EASY [5] that implements a multilevel structure based on evolutionary algorithms [6]. The optimization problem is concerned with the design of the shower plate for minimum non-uniformity (NU) of the growth rate across the substrate. The design variables are
Fig. 1. 5-variable parameterization of the shower plate.
Table 1. Shape-optimization problem: range and optimal
values of the design variables.
Design variable Minimum value Maximum value Optimal value R1 (mm) 1 28 6.806 R2’ 0 1 0.115 r1 (mm) 0.250 0.635 0.631 r2 (mm) 0.250 0.635 0.362 r3 (mm) 0.250 0.635 0.262
depicted in Fig.1, while the range of their values is summarized in Table 1. The optimal values of the design variables that correspond to the minimum value of the objective function (NU = 4.27%) are also shown in Table 1. There seems to be a preference of the algorithm to use holes with the maximum permissible value of diameter in the inner zone, and in contrast, holes with the minimum possible value of diameter in the outer ring.
Fig. 2 presents the distribution of the growth rate for the actual and the optimal design of the shower plate. The non-uniformity of the growth-rate distribution decreases from NU=7.52% in the actual design to NU=4.27% in the optimal design. Further improvement in growth-rate uniformity is desirable if the actual restrictions set by the end users of the films are to be restricted. This calls for trying alternative shape-optimization scenario, involving more and carefully selected geometric parameters.
Fig. 2. Growth-rate distribution in the radial direction of the 58mm-substrate for actual and optimal design of the
shower plate. ACKNOWLEDGEMENTS
Financial support was provided by the General Secretariat for Research and Technology of Greece and by the French Ministry of Foreign Affairs through the Programme for “Greece - France cooperation in Research and Technology” (contract 15207XG, 2006-2008).
REFERENCES
1. R.P. Parik, R.A. Adomaitis, M.E. Aumer, D.P. Partlow, D.B. Thomson, G.W. Rubloff, J. Cryst. Growth, 2006, 296, 15.
2. T.C. Xenidou, A.G. Boudouvis, N.C. Markatos, D. Samélor, F. Senocq, N. PrudHomme, C. Vahlas, Surf. Coat. Tech. 2007, 201, 8868.
3. T.C. Xenidou, A.G. Boudouvis, D.M. Tsamakis, N.C. Markatos, J. Electrochem. Soc. 2004, 151, C757.
4. CHAM Ltd, PHOENICS software, www.cham.co.uk. 5. http://velos0.ltt.mech.ntua.gr/EASY/,
6. I.C. Kampolis, K.C. Giannakoglou, Comput. Methods Appl. Mech. Engrg. 2008, 197:2963.
R1 R2=f(R1,R2’) Rmax=30mm r1 r2 r3 R1 R2=f(R1,R2’) Rmax=30mm r1 r1 r2 r2 r3 r3 220 225 230 235 240 245 250 -0,03 -0,02 -0,01 0 0,01 0,02 0,03 Distance in the radial direction (m)
G ro w th r a te ( A /m in ) actual design optimal design 220 225 230 235 240 245 250 -0,03 -0,02 -0,01 0 0,01 0,02 0,03 Distance in the radial direction (m)
G ro w th r a te ( A /m in ) actual design optimal design
